1. Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly p
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Question
1. Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function.
P(x) = 12x2 + 1992x 53,000
To maximize the monthly rental profit, how many units should be rented out?
What is the maximum monthly profit realizable?
2. The average speed of a vehicle on a stretch of Route 134 between 6 A.M. and 10 A.M. on a typical weekday is approximated by the function
f(t) = 23t 46sqroot(t)+ 56 (0 t 4)
where f (t) is measured in miles per hour, and t is measured in hours, with t = 0 corresponding to 6 A.M. At what time of the morning commute is the traffic moving at the slowest rate?
What is the average speed of a vehicle at that time?
Explanation / Answer
1) 0<=x<=100
P(x) = 12x2 + 1992x 53,000
for local maximum dP/dx =0
dP/dx =-24x +1992 -0 =0
=>x =1992/24
=>x =83
P(0)=0+0 -53000=-53000
P(83)=12*832 + 1992*83 53,000=29668
P(100)=12*1002 + 1992*100 53,000=26200
To maximize the monthly rental profit, 83 units should be rented out
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